A certain compound containing only carbon and hydrogen was found to have a vapor density of 2.550 g/L at 100 degrees C and 760 mm Hg. If the empirical formula of this compound is CH, what is the molecular formula of this compound?
I had some ideas as to how to solve this problem.
First, I thought of using the Specific Heat Formula to find a value, that could resemble a known element.
Q = m CP delta T
1 = m(2.550)(373.15)
1 = m(951.53)
m = 0.00105 g
At this point, I'm really stuck. I know that to find the molecular formula of a compound, I need to divide the empirical mass over the molecular mass. However, I am not sure how to find both masses. I was thinking to find the empirical mass I could calculate CH.
C = 14.011 g
H = 1.007 g
CH = 14.011 + 1.007 = 15.018 g
This appears to be the molecular mass, but I still need the molecular mass.
P V = n R T
You know P, V is one liter, you know T and R
so solve for n
n is the number of moles of the gas (it will be a small fraction of a mole) in 2.55 grams
or the compound is 2.55/n grams per mole
CH you said is 15 grams per mole
If it were C2H2 it would be 30 grams per mole etc
You used the wrong atomic weight for C. It is 12.011, not 14.011
I'm still unsure as to how to find the molecular formula. I found the number of moles of CH.
To determine the molecular formula of a compound, we need to know both the empirical formula (which you have already determined as CH) and the molar mass of the compound.
To calculate the molecular mass, we need to find the actual molar mass of the compound based on the given information. The vapor density of a substance can be used to determine its molar mass.
The vapor density (ρ) is defined as the mass of a substance (in grams) divided by its volume (in liters) at a given temperature and pressure. In this case, the vapor density is given as 2.550 g/L.
We can use the ideal gas law to relate the vapor density to the molar mass of the compound:
ρ = (molar mass)/(molar volume)
Since the molar volume of an ideal gas at standard conditions (100 degrees C and 760 mm Hg) is 22.4 L/mol, we can rearrange the equation as follows:
molar mass = ρ x molar volume
Substituting the given values:
molar mass = 2.550 g/L x 22.4 L/mol
molar mass = 57.12 g/mol
Now we have the molar mass of the compound, which is 57.12 g/mol.
To find the molecular formula, we need to compare the empirical formula mass (15.018 g/mol, calculated earlier) with the molar mass (57.12 g/mol).
To do this, we divide the molar mass by the empirical formula mass:
57.12 g/mol ÷ 15.018 g/mol = 3.8
This means that the ratio of the molar mass to the empirical formula mass is approximately 3.8.
Finally, we multiply the subscripts of the empirical formula by this ratio to obtain the molecular formula:
C1H1 x 3.8 = C3.8H3.8
Since we can't have fractional subscripts in a molecular formula, we need to round them to the nearest whole number. Therefore, the molecular formula of the compound is C4H4.